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A168327
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Primes of concatenated form "1 n^3".
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16
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11, 127, 12197, 135937, 159319, 11092727, 11295029, 11860867, 12685619, 14330747, 14826809, 15000211, 15929741, 16128487, 18869743, 19393931, 124137569, 126198073, 127818127, 129503629, 138958219, 150243409, 154439939
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OFFSET
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1,1
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COMMENTS
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(1) It is conjectured that sequence is infinite.
(2) These are primes all with "leading" digit "1", they are concatenations of two cubic numbers: 1^3 and n^3, n is a natural.
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REFERENCES
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Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996
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LINKS
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FORMULA
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If n^3 is a d-digit number and d no multiple of 3, then p=10^d+n^3, where n is odd and no multiple of 5.
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EXAMPLE
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(1) 10^1+1^3=11 = prime(5) = a(1).
(2) 10^2+3^3=127 = prime(31) = a(2).
(3) 10^4+13^3=12197 = prime(1458) = a(3).
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MATHEMATICA
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Select[FromDigits[Join[{1}, IntegerDigits[#]]]&/@(Range[500]^3), PrimeQ] Harvey P. Dale, May 16 2012
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 23 2009
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EXTENSIONS
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STATUS
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approved
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